This exercise uses the radioactive decay model. after 3 days a sample of radon-222 has decayed to 58% of its original amount. (a) what is the half-life of radon-222? (round your answer to two decimal places.) days (b) how long will it take the sample to decay to 15% of its original amount? (round your answer to two decimal places.) days

a) 3.85 days

b) 10.54 days

Explanation:-

Expression for rate law for first order kinetics is given by:

where,

k = rate constant  = ?

t = time taken for decomposition  = 3 days

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process  =

First we have to calculate the rate constant, we use the formula :

Now put all the given values in above equation, we get

a) Half-life of radon-222:

Thus half-life of radon-222 is 3.85 days.

b) Time taken for the sample to decay to 15% of its original amount:

where,

k = rate constant  =

t = time taken for decomposition  = ?

a = let initial amount of the reactant  = 100 g

a - x = amount left after decay process  =

Thus it will take 10.54 days for the sample to decay to 15% of its original amount.

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